1 - 1 © 2012 Pearson Education, Inc.. All rights reserved. Section 1.1 Slopes and Equations of...

1 - 1

© 2012 Pearson Education, Inc.. All rights reserved.

Section 1.1Slopes and

Equations of Lines

How are linear relationships used to model and solve real

world problems?

1 - 2 © 2012 Pearson Education, Inc.. All rights reserved.

Match each term to a correct description.

Terms Descriptions1. point-slope form A. Where x- and y- axes cross.

2. Horizontal line B. Graph with No slope

3. Vertical line C. Slopes are the same

4. Perpendicular lines D. x-coordinate is negative and y-coordinate is negative

5. Parallel lines E.

6. 2nd Quadrant F. Has two axes and four quandrants

7. 3rd Quadrant G. Slopes are opposite reciprocals

8. Cartesian Coordinate Plane H. Graph has slope of zero

9. Origin I. x-coordinate is negative and y-coordinate is positive.

11 xxmyy

How are linear relationships used to model and solve real world problems?


Quadrants



Intercepts & Slopes




3,2 and 8,9given line theof slope theFind :Example


Possible Slopes of lines



Your Turn 1 – Check for Understanding

Find the slope of the line through (1,5) and (4,6).

1 1 2 2 Let ( , ) (1,5) andSol ( ,ut )ion: (4,6). x y x y

Use the definition of the slope .ymx

6 54 1

13



Writing Equations



Examples: Find an equation of a line who passes through the points (8,9) and (-2,3)



Figure 5




Find the equation of the line with x-intercept − 4 and y-intercept 6. Solution: Notice that b = 6. To find m, use the definition of the slope after writing the x-intercept as (− 4, 0) and y-intercept as (0,6).

Substituting these values into y = mx + b, we have

0 6 6 34 0 4 2

m

3 6.2

y x




Find the slope of the line whose equation is 8 3 5.x y

To find the slope, solve the equatiSolution on f: or y.8 3 5x y

Subtract 8 from3 8 5 both sides. y x x

Divide both si8 5 3

des b 33

y . y x

The coefficient of is 8 / 3, which is the slope of the line. x




Find the equation of the line through (2,9) and (5,3). Put your answer in slope-intercept form.

Begin by using the definition of slope of the line that passes through the giveSo

n lution

poi:

nts.3 9 6 25 2 3

m

Either (2,9) or (5,3) can be used in the point-slope form with 2.m

1 1

1 1

1 1

If ( , ) (2,9), then ( )

9 2( 2)

9, 2, 2 y x

x yy y m x x

y m x

9 2 4 Distributiv e Propertyy x

2 13 Add 9 b ot h sidesy x



Assessment Prompt

Ones do Page 13 #1,7,11,15,19 Twos do Page 13 #3,5,9,17,21

Check each other’s work….Be prepared to defend your answers.



A Quick Review



Homework

Page 13 #2-12 even & #16-24 even



Parallel & Perpendicular lines



Your Turn 5

Find the equation of the line that passes through the point (4,5) and is parallel to the line 3 6 7.x y

The slope of 3 6 7 can be found by writing the equation in slope-intSolutio

ercept form.n

: x y

subtract 3 from both sides a3 6 7

6 3 7 3 7

nd

and divid 6 6

e both sides by 6.

1 72 6

xx y

y x

y x

y x

The result shows that the slope is 1/ 2. Since the linesare parallel, 1/ 2 is also the slope of the line whose equationwe want. cont inued



Your Turn 5 continued

1 1

1 1

This line passes through (4,5). Substituting 1/ 2,4 and 5 into the point-slope form give

(s

)y

mx y

y m x x

1 1

1 1

This line passes through (4,5). Substituting 1/ 2,4 and 5 into the point-slope form giv s

( ).e

y xx

y

m

m xy

1 2 5 Add 5 to both sid e .2

sy x

1 3 2

y x



Your Turn 6

Find the equation of the line that passes through the point (3,2) and is perpendicular to the line 2 3 4.x y

To find the slope, write 2 3 4 in slope-intSolut

erceion

pt r:

m:

fox y

subtract 2 from both sides2 3 43 2 4

2 4 3 3

and

and divide both sides by 3.

x yy x

y

x

x

The slope is 2 / 3. Since the lines are perpendicular, if line 2has slope , then 1

33 / 2. continued

L

m m

m



Your Turn 6 continued

1 1

1 1

Now subtitute 3 / 2, 3 and 2 into the point-slope( )

form.y y m

m x yx x

32 ( 3)2

y x

3 92 Distri 2

butive propert2

yy x

Add 2 to both sides and ge3 9 +2 2 23 5

t a

common de 2 2

nominator.

y x

y x



Assessment Prompt

Think-Pair-Share Page 13 #13,14,29,31,33 Check each other’s work….Be prepared to defend your

answers.



Applications

The table on the left lists the average annual cost (in dollars) of tuition and fees at public four-year colleges for selected years.

a) Plot the cost of public colleges by letting t = 0 correspond to 2000. Are the data exactly linear?

b) Use the points (0,3508) and (9,7020) to determine an equation that models the data.

c) How accurate is this equation in representing the cost of public colleges? Explain in context.



Graph of Tuition and Fees



Assessment Prompt

Think-Pair-Share Page 16 #71 Check each other’s work….Be prepared to defend your

answers.



Lesson Assignment

News/Talk Radio Math Modeling

Find a linear equation to model the number of stations carrying News/Talk Radio

Explain, in words, your process of finding this linear equation.

Predict the number of stations carrying news/talk radio in 2008. Compare this number with the actual amount.

Predict the number of stations carrying news/talk radio in 2020. How confidant can you be about your prediction?



Homework Pages 13-16 #26-38even, and

#50,52,58,62,64,66,68


Exit Ticket:Why is slope important?

1 - 1 © 2012 Pearson Education, Inc.. All rights reserved. Section 1.1 Slopes and Equations of...

Documents

Transcript of 1 - 1 © 2012 Pearson Education, Inc.. All rights reserved. Section 1.1 Slopes and Equations of...